ratios and rates notes - ms. burton's resource...
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Ratios and Rates Notes
1
Ratios and Rates
Essential Vocabulary
Ratio: A ratio is a comparison of two numbers usingdivision. A ratio that compares a to b can be written in three different ways.
a. Words a to b
b. Fraction
c. Colon a : b
?
ab
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Ratios and Rates Notes
2
Examples: Write each examples as a ratio in three different ways. Write the ratio in both nonsimplified form and in simplest form.
a. There are 14 boys and 10 girls in class. Compare the number of boys in class to the number of girls in class.
Examples: Write each examples as a ratio in three different ways. Write the ratio in both nonsimplified form and in simplest form.
b. Three out of five dentists prefer Brand X toothpaste. Compare the dentists who prefer Brand X to the number of dentists who do not.
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Ratios and Rates Notes
3
Examples: Write each examples as a ratio in three different ways. Write the ratio in both nonsimplified form and in simplest form.
c. 85 people surveyed preferred Jiff peanut butter and 15 people preferred Skippy peanut butter. Compare the number of people who preferred Jiff to the total number surveyed.
Equivalent Ratios
Equivalent ratios are ratios that have the same value.
For example and are equivalent because
= 1.25 and = 1.25
1512
2520
1512
2520
?
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Ratios and Rates Notes
4
Examples: Determine if the following ratios are equivalent
a. and
b. 25 to 2.5 and
c. and
1810
3 : 1 23
20 2
15 3 11 : 2
26
56
Rate: A rate is a ratio of two quantities that have
different units.
Equivalent rates: Equivalent rates are two rates
that have the same values.
More Essential Vocabulary
?
?
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Ratios and Rates Notes
5
Examples: Write a rate for each situation, and create an equivalent rate with the given conditions.
A. Sue types 75 words per minute.
a. Write and properly label a rate.
b. How many words can Sue type per hour?
Examples: Write a rate for each situation, and create an equivalent rate with the given conditions.
B. Lightning strikes about 100 times per second around the world.
a. Write and properly label a rate.
b. About how many times does lightning strike per minute around the world.
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Ratios and Rates Notes
6
Examples: Write a rate for each situation, and create an equivalent rate with the given conditions.
C. Materials cost $0.87 for 30 inches.
a. Write and properly label a rate.
b. How much money could that be per foot?
Examples: Write a rate for each situation, and create an equivalent rate with the given conditions.
D. The object moved 15 meters in 5 minutes.
a. Write and properly label a rate.
b. How many centimeters would that be per hour?
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Ratios and Rates Notes
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Unit Rate
A unit rate is a rate that has a denominator of 1 unit.
To write an equivalent rate, find an equivalent rate with a denominator of 1 unit. To find a unit rate, divide the distance (or frequency) by the amount of time (or number of units).?
?
?
Examples: Write each situation as a unit rate.
a. 24 pages in 15 minutes
b. 18 degrees in 6 minutes
c. 3 lbs. for $2
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Attachments
Rates and Proportions Vocabulary.doc
Rates, Ratios, and ProportionsVOCABULARY
Word
Definition
Example
1
Congruent
Same size and shape; corresponding sides and angles are equal
(Symbol:
)
@
4
1
1
4
1
5
1
5
=
·
=
·
EMBED Equation.3
DEF
ABC
D
@
D
2
Convert (conversion)
To change from one form to another
Time conversion: 1 minute = 60 seconds
Length conversion: 12 inches = 1 foot
3
Corresponding
In similar figures, parts that in the same location and are in proportion
SA corresponds to MO
OR corresponds to AL
4
Cross multiplying
One method to prove proportions are equal
15
10
9
6
=
90
90
10
9
15
6
=
·
=
·
5
Customary system
A system of measurement in the U.S.
Length: inch, foot, yard mile
Capacity: ounce, cup, pint, quart, gallon
Weight: ounce, pound, ton
6
Equivalent rates
Rates that have the same value (are equal)
min
1
5720
1
65
feet
hour
miles
=
4
1
1
4
1
5
1
5
=
·
=
·
Because
mile
feet
hour
hour
miles
1
5280
min
60
1
1
65
·
·
7
Equivalent ratios
Ratios that have the same value (are equal)
24
15
8
5
and
are equivalent ratios because both ratios equal 0.625
8
Formula
A mathematical statement or rule
Convert 40 degrees Celsius to degrees Fahrenheit using the formula
32
5
9
+
=
C
F
:
F
F
0
104
32
)
40
(
5
9
=
+
=
9
Indirect measurement
A technique that uses proportions to find a measurement when direct measurement is not possible
On a map, 1 inch = 25 miles. If a distance between two cities is 8 inches, how many miles is it?
miles
inches
miles
inch
?
8
25
1
=
miles
x
miles
x
200
8
25
=
·
=
10
Metric
A system of measurement based on tens
Kilo- Hecto- Deka- (base) Deci- Centi- Milli-
Base units
Capacity: liter
Length: meter
Mass: gram
11
Multiplicative Identity Property
Any number multiplied by one will always give a product of the original number (the number keeps its identity)
12
Percent
A ratio meaning “out of 100” (Symbol: %)
%
40
100
40
=
%
75
100
75
20
15
=
=
13
Polygon
A closed figure formed from line segments that meet only at their endpoints
Examples Non-Examples
14
Proportion
An equation that states that two terms are equal
18
15
6
5
=
a
a
b
a
13
5
52
20
=
15
Rate
A fixed ratio between two things
Cell phone plan: 8 cents/minute
Bag of candy: $1.49/lb
16
Ratio
A comparison of two numbers; can be written in words, as a fraction, or with a colon
There are 3 boys and 4 girls in the class. What is the ratio of boys to girls?
Words 3 to 4
Fraction
4
3
Colon 3:4
17
Similar
Figures that are the same shape but not necessarily the same size
(Symbol: ~)
18
Standard system
Another name for the customary system
Length: inch, foot, yard mile
Capacity: ounce, cup, pint, quart, gallon
Weight: ounce, pound, ton
19
Unit Analysis
The mathematical process used to convert from one measurement to another
Convert 25 miles per hour to feet per second
sec
1
3
2
36
sec
3600
1
1
5280
1
25
feet
hour
mile
feet
hour
miles
=
·
·
20
Unit Rate
A rate that has a denominator of one unit
Apples cost
lbs
1
79
.
0
$
Speed limit is
hour
miles
1
65
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